||Time: 1 hour
- If and g(x)=x-1, let h(x)=f(g(x)).
Answers: The function , with interval of domain .
h(2)=1, and h(0) is undefined.
- Find h(x).
- What is the domain of h(x)?
- Find h(2) and h(0).
- Let A=(3,1), B=(7,-4) and C=(10,9).
- Find an equation of the line passing through the points A and B.
- Find an equation of the line parallel to the line in the first part that passes through the point C.
- Find an equation of the line perpendicular to the line in the first part that passes through the point B.
Answers: An equation for the first line is
for the second line
and for the third line
- What is the vertex of the graph of the parabola ?
Also: Describe how you would translate the graph so that the vertex is moved to the origin.
Answers: The vertex is located at . To move the vertex to the origin, you have to shift up by units and to the left by units.
- Solve the equation .
- Solve the inequality . Express your answer in interval form.
Answers: The equation has the solutions x=0, x=-1 and x=4.
The inequality has at its solution set the union of the intervals and .
- A chemist mixes a 12% hydrochloric acid solution with a 5% hydrochloric acid solution. How many milliliters of each solution should the chemist use to make a 500 ml liter solution that is 8% hydrochloric acid?
Answer: The exact answer is ml of the 12% solution and ml of the 5% solution. The approximate answer is 214.29 ml of the 12% solution and 285.71 ml of the 5% solution.
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Thu Jun 12 22:58:04 MDT 1997
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